Accurate seismic imaging of the earth's subsurface is crucial to the oil and gas industry. Seismic images are used, for instance, to determine the locations, types and characteristics of various subsurface formations, thereby facilitating hydrocarbon discovery and production including reservoir management such as well placement. Seismic imaging generally entails using a seismic source, such as a controlled explosion, to provide seismic waves into the subsurface of interest. The subsurface typically has numerous layers or formations, and each layer or formation has different characteristics, including the velocity at which seismic waves pass through. For example, seismic wave velocity in a sediment layer may be 7,500 feet per second, while an adjacent salt layer velocity may be 14,750 feet per second. For the purposes of this paper, a sediment layer may be unconsolidated sediment or consolidated sediment having relatively low seismic wave velocity as compared to distinct formations such as salt bodies with relatively high seismic wave velocity.
When seismic waves reach the boundaries between layers having different velocity profiles, some of the energy in waves are reflected off a boundary and echo back toward the surface. The remaining energy in the waves passes through the boundary and propagates toward the next boundary, and the process repeats. Many imaging techniques, including depth migration techniques such as reverse time migration (RTM), use the reflected energy recorded at the surface to image the subsurface rock boundaries.
High-contrast velocity boundaries (e.g., water-sediment and sediment-salt boundaries) cause several types of problems in an RTM image: (1) the introduction of backscattering noise, which is typically caused by the upward-bound energy present in the modeled wavefields due to reflections at the high-contrast boundaries; (2) wavelet distortion, which is caused by a longer wavelength on the higher velocity side of a boundary and a shorter wavelength on the lower velocity side of the boundary; (3) mis-position of the boundaries, typically caused by traditional smoothing techniques that alter the velocity near and above the boundary: and (4) discretization grid stair-casing diffraction noise. Smoothing is sometimes used to mitigate these concerns, but it does so inadequately.